The area of a field in the shape of a hexagon is `2400 sqrt(3) m^(2)` . What will be the cost of fencing it at Rs. 18.50 per metre?

Options

A. a)Rs. 4440
B. b)Rs. 5920
C. c) Rs. 5550
D. d) Rs. 5180

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Area of the Hexagon
The area of a regular hexagon can be expressed in terms of the side length \( a \) using the formula:
\[ \text{Area} = \frac{3\sqrt{3}}{2} a^2 \]
Given that the area of the hexagon is \( 2400 \sqrt{3} \, m^2 \), we can set up the equation:
\[ \frac{3\sqrt{3}}{2} a^2 = 2400 \sqrt{3} \]

### Step 2: Simplify the Equation
To eliminate \( \sqrt{3} \) from both sides, we divide both sides by \( \sqrt{3} \):
\[ \frac{3}{2} a^2 = 2400 \]

### Step 3: Solve for \( a^2 \)
Next, we multiply both sides by \( \frac{2}{3} \) to isolate \( a^2 \):
\[ a^2 = 2400 \times \frac{2}{3} = 1600 \]

### Step 4: Find the Length of One Side \( a \)
Now, we take the square root of both sides to find \( a \):
\[ a = \sqrt{1600} = 40 \, m \]

### Step 5: Calculate the Perimeter of the Hexagon
The perimeter \( P \) of a regular hexagon is given by:
\[ P = 6a \]
Substituting the value of \( a \):
\[ P = 6 \times 40 = 240 \, m \]

### Step 6: Calculate the Cost of Fencing
The cost of fencing per meter is given as Rs. 18.50. Therefore, the total cost \( C \) for fencing the entire perimeter is:
\[ C = P \times \text{Cost per meter} = 240 \times 18.50 \]

### Step 7: Perform the Final Calculation
Calculating the cost:
\[ C = 240 \times 18.50 = 4440 \, \text{Rs} \]

### Final Answer
The cost of fencing the hexagon is Rs. 4440.

---